Question - For each of the following software project phases, suggest a design model or representation that would be a helpful aid in the design process.

Your opponent is allowed to send you two plaintext messages M0 and M1, each n letters long. You now pick a new private key K, resulting in a new pseudo-random permutation EK : {A, . . . , Z} {A, . . . , Z}. You also pick uniformly at random a private bit b {0, 1} and return a ciphertext C = c0c1 . . . cn, namely the message Mb encrypted with cipher-block chaining using the fresh EK. Finally, your opponent has to guess your bit b. Approximately how large must n be at least for your opponent to have a greater than 75% chance of guessing b correctly? Outline a strategy that your opponent can use to achieve this. This is an example only. StudentNames[1:30] [1] (ii) Many correct answers, they must be meaningful. This is an example only. StudentMarksTest1[1:30] StudentMarksTest2[1:30] StudentMarksTest3[1:30] (1 mark) StudentTotalScore[1:30] (1 mark) [2] (b) (i) - outside loop zeroing total for loop (sum in example below) - loop for all students - input name and all test scores - in loop adding a student's total - storing the total - inside loop printing student's name and total - outside loop calculating class average - printing class average sample algorithm: [8] (ii) any relevant comment with regards to efficient code (e.g. single loop) [1] (c) Many correct answers, these are examples only. 1 mark per data set and reason Set 1: 20, 25, 35 Reason: valid data to check that data on the upper bound of each range check is accepted Set 2: 21, 26, 36 Reason: invalid data to check that data above the upper bound of each range check is rejected [2] Give and clearly explain a formula that expresses the optimal solution in terms of optimal solutions to subproblems. [Note: If your formula gives only a scalar metric (e.g. the number of stamps) rather than the actual solution (e.g. which stamps), please also explain how to obtain the actual optimal solution.] [4 marks] (ii) Draw and explain the data structure your algorithm would use to accumulate the intermediate solutions. [2 marks] (iii) Derive the big-Theta space and time complexity of your algorithm. [1 mark] (b) Repeat (a)(i)-(a)(iii) for the following problem: A car must race from point A to point B along a straight path, starting with a full tank and stopping as few times as possible. A full tank lets the car travel a given distance l. There are n refuelling stations so A, s1, s2, . . . , sn B along the way, at given distances d0 = 0, d1, d2, . . . , dn from A. The distance between adjacent stations is always less than l. 6 CST.2014.2.7 6 Software and Interface Design The following is an extract from a design brief written by the client for one of the 2014 Cambridge group design projects. What I'd like is some sort of database of recipes to which I can send queries such as "Find me something that doesn't contain cabbage or tomatoes that takes less than 30 minutes to prepare", or "I've got kohlrabi in the veg box AGAIN, are there any recipes I haven't tried that might make something edible out of it?", or "I've actually got a couple of hours free to cook this weekend, what was that complicated Ottolenghi recipe I flagged two weeks ago to try later?". The database needs to cope with the fact that ingredients can have different names but mean the same thing: e.g. "flour" and "plain flour", and that "1/4 lb" and "4oz" are the same thing and equal to "100g" (and not 113g). It would be great if once I've chosen this week's menu, it could produce a shopping list I can plug into www.myfavouritesupermarket.com, and it needs to be usable by non-engineers. (a) For each of these, sketch an example to show what this model looks like, based on some part of the above design brief. (i) Inception phase (ii) Elaboration phase (iii) Construction phase (iv) Transition phase [12 marks] (b) For each of the sketched examples in part (a), describe how the design work so far could be evaluated before proceeding to the next phase. [4 marks] (c) Choose two of the above design models, representations or evaluation methods, and explain how they would be done differently if the design project was following an agile rather than spiral project management approach. [4 marks] 7 (TURN OVER) CST.2014.2.8 SECTION D 7 Discrete Mathematics (a) Let m be a fixed positive integer. (i) For an integer c, let Kc = { k N | k c (mod m) }. Show that, for all c Z, the set Kc is non-empty. [2 marks] (ii) For an integer c, let c be the least element of Kc. Prove that for all a, b Z, a b (mod m) iff a = b. [4 marks] (b) (i) State Fermat's Little Theorem. [2 marks] (ii) Prove that for all natural numbers m and n, and for all prime numbers p, if m n (b) if ever req is high and started is low then eventually error will become permanently high [2 marks] Briefly describe the main ideas underlying model checking. What is symbolic model checking? [4 + 4 marks] Compare and contrast the use of a model checker and a theorem prover for formal verification.